A cone of height `8 m` has a curved surface area `188.4` square metres. Find its volume. (Take `pi = 3.14`)

Explanation

Let the base radius be `r` metres and slant height be `l` metres
Then,
curved surface area `= pi rl = pi r sqrt(r^(2) + h^(2))`
`= (3.14 xx r xx sqrt(r^(2) + 64)) m^(2)`
`:. 3.14 xx r xx sqrt(r^(2) + 64) = 188.4`
`rArr r sqrt(r^(2) + 64) = (188.4)/(3.14) = 60`
`rArr r^(2) (r^(2) + 64) = 3600`
`{:(rArr,r^(4) + 64r^(2) - 3600 = 0),(rArr,(r^(2) + 100) (r^(2) - 36) = 0):} " " [( :' x^(2) + 64x - 3600 =0 ", where" r^(2) = x),(rArr(x + 100) (x - 36) = 0)]`
`rArr r^(2) = 36 [ :' r^(2) = - 100 " given imaginary value of r"]`
`rArr r = 6`
So, the radius of the base `= 6 m`
Volume `= ((1)/(3) pi r^(2)h)` cubic units
`= ((1)/(3) xx 3.14 xx 6 xx 6 xx 8) m^(3) = 301.44 m^(3)`
Hence, the volume of the cone is `301.44 m^(3)`